Question

So the question is basically asking which mountains peaks can be seen from Oahu.

Island Distance(Mi) Mountain Height(ft)
Lanai - 65 - Lanaihale - 3,370
Maui - 110 - Haleakala - 10,023
Hawaii - 190 - Mauna Kea - 13,796
Molokai - 40 - Kamakou - 4,961

A) Radius of earth= 3960 mi.
Determine angle formed at the center of the earth.
B) Determine length of the hypotenuse.
Is Lanai-hale visible from Oahu?
C) Repeat parts A & B for the other 3 islands
D) Which 3 Mountains are visible from Oahu?
Can someone please draw a diagram and explain to me where the angle formed at the center of the earth and hypotenuse please? I'm really despearate to understand this problem! It's due on Monday! please help! xoxoxo <3

Answer 1

If you draw a line from a point above the surface, to the horizon, the angle where the radius meets the point on the horizon is a right angle, because the line is tangent to the surface of the earth.

So, if you have a point x km above the surface, and the radius of the earth is r km, and the distance from the point to the horizon is d km,

r^2 + d^2 = (r+x)^2
If you need to work with the angle θ at the center of the earth,

sinθ = d/(r+x)
tanθ = d/r

Answer 2

if the first three terms in the expansion of (1+ax)^n in ascending powers
of x are 1+12x+64x^2 find n and a